Heightened Review Linear Equations/Functions-shurig

1) Which is a linear function?

F(x)

G(x)

H(x)

I(x)

A linear function is a function that can be represented by a straight line on a graph. In the given options, i(x) is the only function that represents a straight line. Therefore, i(x) is the correct answer as it is the only linear function among the options provided.

Explanation

A linear function is a function that can be represented by a straight line on a graph. In the given options, i(x) is the only function that represents a straight line. Therefore, i(x) is the correct answer as it is the only linear function among the options provided.

2) Which function is nonlinear?

not-available-via-ai

Explanation

not-available-via-ai

3) Limousine Company P and Company R both charge a rental fee plus an additional charge per hour.
The equation y = 50 + 30x models the total cost (in dollars), y, of renting a limousine from Company P for x hours.
The table below shows the cost to rent a limousine from Company R for different lengths of time.
Which statement accurately compares the per hour charges of the two companies?

Company P charges $5 less per hour than Company R.

Company P charges $5 more per hour than Company R

Company charges $25 less per hour than Company R

Company P charges $25 per hour than Company R.

not-available-via-ai

Explanation

not-available-via-ai

4) Tremain uses the point (2, 26) and (4, 30) to write the equation of a line that relates the number of new cell phones, y, his stores sells to the number of hours, x, the store has been open. What equation should Tremain write?

Tremain can use the formula for the equation of a line, y = mx + b, where m is the slope and b is the y-intercept. To find the slope, he can use the formula (y2 - y1) / (x2 - x1), substituting the coordinates (2, 26) and (4, 30). The slope is (30 - 26) / (4 - 2) = 2. Therefore, the equation Tremain should write is y = 2x + b. To find the value of b, he can substitute the coordinates of one of the points, such as (2, 26), and solve for b.

Explanation

Tremain can use the formula for the equation of a line, y = mx + b, where m is the slope and b is the y-intercept. To find the slope, he can use the formula (y2 - y1) / (x2 - x1), substituting the coordinates (2, 26) and (4, 30). The slope is (30 - 26) / (4 - 2) = 2. Therefore, the equation Tremain should write is y = 2x + b. To find the value of b, he can substitute the coordinates of one of the points, such as (2, 26), and solve for b.

5) Rain is flowing into two containers at different rates. The figure shows the volume of water in each container at different times. What is the difference in the rate of change between the two containers?

The difference in the rate of change between the two containers can be determined by comparing the slopes of the lines representing the volume of water in each container. If the slope of one line is steeper than the other, it indicates a higher rate of change in that container. Conversely, if the slope is less steep, it suggests a slower rate of change. By visually inspecting the figure, we can observe that the slope of the line representing the first container is steeper than the slope of the line representing the second container. Therefore, the first container has a greater rate of change compared to the second container.

Explanation

The difference in the rate of change between the two containers can be determined by comparing the slopes of the lines representing the volume of water in each container. If the slope of one line is steeper than the other, it indicates a higher rate of change in that container. Conversely, if the slope is less steep, it suggests a slower rate of change. By visually inspecting the figure, we can observe that the slope of the line representing the first container is steeper than the slope of the line representing the second container. Therefore, the first container has a greater rate of change compared to the second container.

6) Alice compared the graphs of two functions.
The first function was y = 3x + 4
The second function fits the values in teh table shown.
What is the distance between the y-intercepts of the two functions?

1

2

3

4

The distance between the y-intercepts of the two functions can be found by subtracting the y-intercept of the first function from the y-intercept of the second function. Since the first function has a y-intercept of 4, and the second function is not given but is represented by the number 3 in the answer choices, the difference between 4 and 3 is 1. Therefore, the distance between the y-intercepts of the two functions is 1.

Explanation

The distance between the y-intercepts of the two functions can be found by subtracting the y-intercept of the first function from the y-intercept of the second function. Since the first function has a y-intercept of 4, and the second function is not given but is represented by the number 3 in the answer choices, the difference between 4 and 3 is 1. Therefore, the distance between the y-intercepts of the two functions is 1.